The bijective soft set with its operations

Soft set theory is a newly emerging tool to deal with uncertain problems and has been studied by scholars in theory and practice. This paper proposes the concept of bijective soft set and some of its operations such as the restricted AND and the relaxed AND operations on a bijective soft set, dependency between two bijective soft sets, bijective soft decision system, significance of bijective soft set with respect to bijective soft decision system, reduction of bijective soft set with respect to bijective soft decision system, and decision rules in bijective soft decision system. With these notions and operations, an application of bijective soft set in decision-making problems is also discussed.

[1]  A. R. Roy,et al.  An application of soft sets in a decision making problem , 2002 .

[2]  Steven Li,et al.  The normal parameter reduction of soft sets and its algorithm , 2008, Comput. Math. Appl..

[3]  Zhi Xiao,et al.  A combined forecasting approach based on fuzzy soft sets , 2009 .

[4]  Naim Çagman,et al.  Soft sets and soft groups , 2007, Inf. Sci..

[5]  Bingxue Yao,et al.  Fuzzy soft sets and fuzzy soft groups , 2008, 2008 Chinese Control and Decision Conference.

[6]  Mustafa Mat Deris,et al.  A Direct Proof of Every Rough Set is a Soft Set , 2009, 2009 Third Asia International Conference on Modelling & Simulation.

[7]  Yan Zou,et al.  Data analysis approaches of soft sets under incomplete information , 2008, Knowl. Based Syst..

[8]  Young Bae Jun,et al.  Soft semirings , 2008, Comput. Math. Appl..

[9]  Daowu Pei,et al.  From soft sets to information systems , 2005, 2005 IEEE International Conference on Granular Computing.

[10]  Feng Feng,et al.  Soft Rough Sets with Applications to Demand Analysis , 2009, 2009 International Workshop on Intelligent Systems and Applications.

[11]  Xiaoyan Liu,et al.  On some new operations in soft set theory , 2009, Comput. Math. Appl..

[12]  Young Bae Jun,et al.  Applications of soft sets in ideal theory of BCK/BCI-algebras , 2008, Inf. Sci..

[13]  D. Molodtsov.  Soft set theory—First results , 1999 .

[14]  A. R. Roy,et al.  Soft set theory , 2003 .

[15]  Young Bae Jun,et al.  Soft set theory applied to ideals in d-algebras , 2009, Comput. Math. Appl..

[16]  Bijan Davvaz,et al.  Soft sets combined with fuzzy sets and rough sets: a tentative approach , 2010, Soft Comput..